Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14271363 | C2 | semidirect |
| 3. #14270916 | C2 | semidirect |
| 4. #14270906 | C2 | semidirect |
| 5. C8×Q8×C29 | C2 | semidirect |
| 34. Q8×C29 | D8 | semidirect |
| 47. C8×C29 | SD16 | semidirect |
| 63. C8×Q8 | D29 | semidirect |
| 81. C29 | #1668 | semidirect |
| 99. Q8 | D232 | semidirect |
| 113. C8 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271540 | 2 |
| #14271363 | 2 |
| #14270916 | 2 |
| #14270906 | 2 |
| C8×Q8×C29 | 2 |
| #1668 | 29 |